Generalized Quantum Search Hamiltonian

Abstract

There are hamiltonians that solve a search problem of finding one of $N$ items in $O(\sqrt{N})$ steps. They are hamiltonians to describe an oscillation between two states. In this paper we propose a generalized search hamiltonian, $H_g$. Then the known search hamiltonians become special cases of $H_g$. From the generalized search hamiltonian, we present remarkable results that searching with 100% is subject only to the phase factor in $H_g$ and independent to the number of states or initialization.

5 pages, Latex

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